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Dergiler / Gazi University Journal of Science / 2020 / Cilt: 33 - Sayı: 3

Well-Defined Solutions of a Three-Dimensional System of Difference Equations

Yasin YAZLIK
Merve KARA
Nouressadat TOUAFEK
Sayfa
767–778
Yayın Tarihi
2022-10-19
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Some numericalexamples are given to demonstrate the theoretical results.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:We show that the three-dimensional system of difference equations𝑥𝑛+1 =𝑎𝑥𝑛𝑧𝑛−1𝑧𝑛−𝛽+ 𝛾, 𝑦𝑛+1 =𝑏𝑦𝑛𝑥𝑛−1𝑥𝑛−𝛾+ 𝛼, 𝑧𝑛+1 =𝑐𝑧𝑛𝑦𝑛−1𝑦𝑛−𝛼+ 𝛽 , 𝑛 ∈ 𝑁0 ,where the parameters 𝑎, 𝑏, 𝑐, 𝛼, 𝛽, 𝛾 and the initial conditions 𝑥−𝑖 , 𝑦−𝑖 , 𝑧−𝑖 , 𝑖 ∈ {0,1}, are nonzeroreal numbers, can be solved.
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Temel Bulgular & Veri:Using the obtained formulas, we determine the asymptoticbehavior of solutions and give conditions for which periodic solutions exist.
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Sonuç & Katkı:Some numericalexamples are given to demonstrate the theoretical results.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

We show that the three-dimensional system of difference equations𝑥𝑛+1 =𝑎𝑥𝑛𝑧𝑛−1𝑧𝑛−𝛽+ 𝛾, 𝑦𝑛+1 =𝑏𝑦𝑛𝑥𝑛−1𝑥𝑛−𝛾+ 𝛼, 𝑧𝑛+1 =𝑐𝑧𝑛𝑦𝑛−1𝑦𝑛−𝛼+ 𝛽 , 𝑛 ∈ 𝑁0 ,where the parameters 𝑎, 𝑏, 𝑐, 𝛼, 𝛽, 𝛾 and the initial conditions 𝑥−𝑖 , 𝑦−𝑖 , 𝑧−𝑖 , 𝑖 ∈ {0,1}, are nonzeroreal numbers, can be solved. Using the obtained formulas, we determine the asymptoticbehavior of solutions and give conditions for which periodic solutions exist. Some numericalexamples are given to demonstrate the theoretical results.

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Bu Makaleye Atıf Yap

YAZLIK, Y., KARA, M., TOUAFEK, N. (2022). Well-Defined Solutions of a Three-Dimensional System of Difference Equations. Gazi University Journal of Science, Cilt: 33 - Sayı: 3, 767–778. https://ajindex.com/articles/521265

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Kaynakça (16)

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